IR absorption band of weak H-Bonded systems: Showcasing the signature of the quantum indirect damping within the framework of a new approach using non-Hermitean Hamiltonian formalism

Abstract

Herein, we investigate the effects of the irreversible action of the medium on the theoretical elucidation of the IR spectrum of weakly H-bonded systems, a prototypical model which provides a rigorous treatment of the relaxation mechanisms impacts on the IR spectral density. The attention will be focused particularly on the effect of indirect damping on the IRυS(X−H⃗) spectrum beyond the harmonic and adiabatic approximations. The ultimate objective of the present investigation is the treatment of the action of the surrounding of the intermonomer modes of H-bonded systems, which must induce a broadening of the Dirac delta peaks, the nature of which, as shown by Maréchal and Witkowski theory, is a Franck–Condon progression. The quantum treatment of the IR absorption band reveals that quantum relaxation of the intermonomer mode of H-bonded complexes could be successfully approached by a non-Hermitian Hamiltonian formalism. Motivated by development of a second method that will be able to validate the first approach, a computationally efficient algorithm was proposed for elucidating the quantum indirect relaxation using Hermitean Hamiltonians. The real eigenvalues, corresponding to different energies of the system are considered to be complex by adjunction of the imaginary parts, which reflects the action of the indirect irreversible action of the medium. These two crude approaches may pave the way for the incorporation of the mechanism of indirect relaxation in more physical and complex situations dealing, particularly, with tunnelling effects in strong H-bonded species, Fermi resonances, and Davydov coupling for cyclic H-bonds dimers beyond the harmonic and adiabatic assumptions.